Field of the Invention
The present invention relates to information processing apparatuses, information processing methods, and storage media.
Description of the Related Art
Classification using support vector machines (SVMs) is employed in a variety of applications and fields, such as image recognition. Regression calculations using support vector regression (SVR) are also employed in such fields. Assuming an input vector to be classified is represented by x, a support vector is represented by xi (where i=1, 2, . . . , n), and a kernel function for vectors x and y is represented by K(x, y), an SVM classification function f(x) can be expressed by Formula (1).
                              f          ⁡                      (            x            )                          =                                            ∑                              i                =                1                            n                        ⁢                                          α                i                            ⁢                              y                i                            ⁢                              K                ⁡                                  (                                      x                    ,                                          x                      i                                                        )                                                              +          b                                    (        1        )            
Here, yi is a supervisory label corresponding to xi, whereas αi and b are parameters determined through learning.
Various types of functions are used as the kernel function K(x, y), such as a linear kernel, a polynomial kernel, an RBF kernel, and so on. A kernel function class known as “additive kernels”, such as the “intersection kernel” described in Subhransu Maji, Alexander C. Berg, and Jitendra Malik, “Classification using Intersection Kernel Support Vector Machine is Efficient”, In IEEE Conference on Computer Vision and Pattern Recognition, 2008 (Non-Patent Document 1), is an example of a frequently-used kernel function. The additive kernel is expressed by Formula (2).
                              K          ⁡                      (                          x              ,              y                        )                          =                              ∑                          d              =              1                        D                    ⁢                      k            ⁡                          (                                                x                  d                                ,                                  y                  d                                            )                                                          (        2        )            
Here, xd and yd represent dth-dimension elements of x and y, respectively, which are D-dimensional vectors. Meanwhile, k(x, y) is a function for calculating an output value from two scalar input variables x and y.
Andrea Vedaldi, Andrew Zisserman, “Efficient Additive Kernels via Explicit Feature Maps”, In IEEE Conference on Computer Vision and Pattern Recognition, 2010 (Non-Patent Document 2), discloses a specific example of an additive kernel. For example, Formula (3) expresses k(x, y) for an intersection kernel, whereas Formula (4) expresses k(x, y) for a X2 kernel.
                              k          ⁡                      (                          x              ,              y                        )                          =                  min          ⁡                      (                          x              ,              y                        )                                              (        3        )                                          k          ⁡                      (                          x              ,              y                        )                          =                              2            ⁢            xy                                x            +            y                                              (        4        )            